of 90
Direct Bends of
Metal–Insulator–Silicon–Insulator–Metal
Waveguides
Volume 5, Number 5, October 2013
Jin-Soo Shin
Min-Suk Kwon
Chang-Hee Lee
Sang-Yung Shin
DOI: 10.1109/JPHOT.2013.2281983
1943-0655 Ó 2013 IEEE
1Department of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST),
Daejeon 305-701, Korea
2School of Electrical and Computer Engineering, Ulsan National Institute of Science and Technology
(UNIST), Ulsan 689-798, Korea
DOI: 10.1109/JPHOT.2013.2281983 1943-0655 Ó 2013 IEEE
Manuscript received August 12, 2013; revised September 6, 2013; accepted September 7, 2013. Date of publication September 16, 2013; date of current version October 1, 2013. This research was supported in part by Basic Science Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2010-0022473) and in part by the 2012 Research Fund of the Ulsan National Institute of Science and Technology (UNIST). Corresponding author: M.-S. Kwon (e-mail: mskwon@unist.ac.kr).
Abstract: We investigate 90 direct bends of metal–insulator–silicon–insulator–metal (MISIM) waveguides, which are hybrid plasmonic waveguides with replaceable insulators. First, we fabricate them using fully standard CMOS technology and characterize them. The experimental excess loss of the two consecutive 90direct bends is 11, 7.4, and 4.5 dB when the width of the Si line of the MISIM waveguide is about 160, 190, and 220 nm, respectively. Second, we analyze the experimental results using the 3-D finite-difference time-domain method. Through the analysis, we investigate possible loss mechanisms of the 90direct bend, which have not been studied to our knowledge. It has been found that the Si lines should be narrow to reduce the excess losses of the 90direct bends. However, the wide Si lines are better for ease of fabrication and for small propagation losses. Finally, we demonstrate a modified low-loss 90direct bend of the MISIM waveguide with a wide Si line.
Index Terms:Plasmonics, silicon nanophotonics, subwavelength structure, waveguides.
1. Introduction
One possible way of overcoming the limit of electronic-only devices is to integrate electronic and photonic devices on a chip scale [1]. However, the dimensions of general photonic devices, which are subject to the diffraction limit, hinder such integration. Nanoplasmonic waveguides can support a mode with surface plasmon polariton nature whose dimensions are much smaller than those of a photonic waveguide mode [2]. Thus, it is expected that nanoplasmonic waveguide devices may alleviate the dimensional mismatch between photonic devices and electronic devices [3]. A variety of nanoplasmonic waveguides have been investigated. A few examples are channel plasmon polariton waveguides [4], dielectric-loaded surface plasmon polariton waveguides [5], [6], and metal–insulator–metal (MIM) waveguides [7]–[10]. However, a typical problem in these nano-plasmonic waveguides is that there is a tradeoff between the degree of mode confinement and the propagation distance. To some extent, the problem is solved by using hybrid plasmonic waveguides [11]–[19], which have a subwavelength mode size and a relatively long propagation distance com-pared with the aforementioned waveguides. Among diverse hybrid plasmonic waveguides, two
kinds of metal–insulator–silicon–insulator–metal (MISIM) waveguides have been actively studied [16]–[19] since they can be realized by using standard CMOS technology. Zhu et al. have studied the covered MISIM waveguide, in which the metal surrounds the horizontal insulator–silicon– insulator stack [18], [19]. We have investigated the uncovered MISIM waveguide, in which the metal sandwiches laterally the horizontal insulator–silicon–insulator stack [16], [17]. Since the top surface of the insulator of this waveguide is exposed, the insulator is removable and replaceable with a functional material.
When nanoplasmonic devices that are based on the MISIM waveguides are developed, in general, they will have waveguide bends. In this paper, we investigate experimentally and theo-retically 90 direct bends of the uncovered MISIM waveguides that have Si lines with widths of about 160, 190, and 220 nm. We show that such wide Si lines are not good for the simple 90direct bends, although they make possible easy fabrication and small propagation losses of the MISIM waveguides. In doing so, we examine the loss mechanisms of the 90direct bends, which have not
yet been studied to our knowledge. In other words, we scrutinize how and why the excess losses of the 90direct bends change depending on the width of the Si line and the distance between the two
consecutive bends. Finally, we propose and analyze a modified 90 direct bend of the MISIM
waveguide with a wide Si line to improve its performance.
2. Fabrication Process and Fabrication Results
The cross-sectional structure of the uncovered MISIM waveguide investigated in this paper is the same as in [17]. It is schematically shown in Fig. 1(a). A Si line of height 250 nm and of width wS is
placed on a buried-oxide ridge of height about 70 nm. Because of the fabrication process used, 10-nm-thick silicon nitride ðSiNxÞ and 50-nm-thick silicon oxide ðSiOxÞ layers are on the Si line. A
SiOx layer that surrounds the SiNxSiOxSi line becomes the insulator of the MISIM waveguide.
The thickness of its horizontal parts is about 40 nm, and that of its vertical parts, i.e., tI, is about
30 nm. On both sides of the SiOxSiSiOx structure, there are copper layers of thickness about
260 nm. The MISIM waveguide supports a hybrid plasmonic mode. The power carried by the mode is strongly confined to the SiOxlayers between the Si line and the Cu layers [16], [17]. To make the
90direct bends of the MISIM waveguides, we used the same fabrication process as in [17], which is based on fully standard CMOS technology. They were made by using an 8-in silicon-on-insulator wafer. The fabrication process consists of low-pressure chemical vapor deposition (LPCVD), KrF (248 nm) lithography, dry etching, high-density plasma chemical vapor deposition (HDPCVD), sputtering, and chemical–mechanical polishing. Thin SiNxand SiOxlayers were deposited by using
LPCVD. We employed HDPCVD to deposit a thick SiOxlayer that was patterned to be a mold for a
copper damascene process. Copper was sputtered to fill the mold and polished chemically and mechanically until the top surface of the insulator was exposed. A scanning electron microscopy (SEM) image of the cross section of the fabricated MISIM waveguide is shown in Fig. 1(b), which is the same as in [17]. To make the overall process simple, we did not include a photoresist trimming
Fig. 1. (a) Schematic diagram of the cross-sectional structure of the realized MISIM waveguide. (b) SEM image of the cross section of the fabricated MISIM waveguide. Pt was just used for the preparation of the cross section, and it is not related to the MISIM waveguide.
process after the KrF lithography. This results in larger values of wSthan those in [18] and [19]. The
resultant values of wS are about 160, 190, or 220 nm since 160 nm is the minimum line width that
can be obtained from the KrF lithography.
Fig. 2(a) schematically shows the structure of the investigated MISIM waveguide with the two consecutive 90direct bends on the xy -plane at z ¼ 195 nm. Fig. 2(b) shows a surface SEM image of the fabricated MISIM waveguide with the 90direct bends. The MISIM waveguide is connected to 450-nm-wide Si photonic waveguides through couplers in which wS increases linearly to 450 nm
over a distance of 600 nm. The 450-nm-wide Si photonic waveguides are connected to 5-m-wide Si photonic waveguides through linear tapering over a distance of 200 m. Light from a source is launched into one 5-m-wide Si photonic waveguide, and light from the other 5-m-wide Si photonic waveguide is detected. The distance between the end of the coupler (position P1) and the
beginning of the 90 direct bend (position P
2) is lM 1. The distance between positions P5 and P6 is
also lM1. The distance between the end of one bend (position P3) and the beginning of the other
(position P4) is lM 2. For the fabricated MISIM waveguide with the 90direct bends, lM 1 ¼ ½ð2 mÞ
wS=2 tI and lM 2¼ ½ð2:5 mÞ wS 2tI. Consequently, the total length of the MISIM waveguide
with the 90 direct bends, which is 2lM 1þ 2ðwSþ 2tIÞ þ lM 2, is fixed at 6.5 m.
3. Measurement and Simulation Results
We measured the fiber-to-fiber insertion losses (in dB) of the combinations of the 5-m-wide Si photonic waveguides, the 450-nm-wide Si photonic waveguides, and the MISIM waveguide with or without the 90 direct bends. The length of the straight MISIM waveguide without the bends is
6.5 m. An excess loss due to the two consecutive bends, denoted by Lb2, is defined as the
subtraction of the insertion loss associated with the straight MISIM waveguide from that associated with the MISIM waveguide with the bends. To measure the fiber-to-fiber insertion losses, we launched light with a wavelength of 1554 nm from a lensed fiber to the facet of one 5-m-wide Si photonic waveguide. Before the light was incident on the lensed fiber, its polarization was adjusted to be transverse electric using a polarization controller. The light coming out from the other 5-m-wide Si photonic waveguide was coupled to another lensed fiber.
The experimental values of Lb2 are in Fig. 3 along with the calculated values. The error bars
represent the standard deviation of the experimental values for the same value of wS. For the
calculation, we used the 3-D finite-difference time-domain (FDTD) method (FDTD Solutions, Lumerical Inc.). For the dielectric constant of copper, we used the model in FDTD Solutions, which is 68:2 þ i10:1 at the wavelength of 1554 nm. While reducing mesh sizes, we checked the convergence of the calculation result. The smallest mesh sizes were 3, 3, and 5 nm along the x -, y -, and z-axes, respectively. We calculated the insertion losses (in dB) of the structure between P1and
P6in Fig. 2(a). They were obtained from the ratios of the power of the light at P6to the power of the
hybrid plasmonic mode, launched at P1, of the MISIM waveguide. We also calculated the
Fig. 2. (a) Schematic diagram of the structure of the MISIM waveguide with the two consecutive 90
direct bends on the xy -plane at z¼ 195 nm. (b) Surface SEM image of the fabricated MISIM waveguide with the 90direct bends. The inset shows an enlarged image of the 90 direct bend. (c) Schematic
diagram of the structure of the MISIM waveguide with one 90 direct bend on the xy -plane at
propagation loss M(in dB=m) of the straight MISIM waveguide. Following the definition of Lb2, we
subtracted ½M ð6:5 mÞ from the insertion losses to obtain the calculated values of Lb2. The
excess loss of one 90direct bend may be approximately half of Lb2, i.e., 5.5, 3.7, and 2.25 dB for
wS ffi 160, 190, and 220 nm, respectively. As reported previously [17], the uncovered MISIM
waveguide with the wide Si line has a smaller propagation loss than the covered MISIM waveguide with the narrow Si line. However, the 90direct bend of the former causes a larger excess loss than
the 90direct bend of the latter, which causes an excess loss of 0:73 0:06 dB when t
I ¼ 28 nm
and wS ¼ 64, 81, 94, or 102 nm [19]. Moreover, the experimental values of Lb2 are quite smaller
than the calculated values. To explain these things and the increase and decrease of Lb2, we
analyze how and why the excess loss of the 90direct bend changes depending on its structural
parameters. This kind of analysis for the MISIM waveguide bends has not yet been done. First, we checked the reflection from one 90direct bend and the transmission through it. For this purpose, we analyzed the MISIM waveguide with just one 90 direct bend, which is schematically shown in Fig. 2(c). Positions Pb and Pc in Fig. 2(c) correspond to P2 and P3 in Fig. 2(a),
respectively. We launched the hybrid plasmonic mode at position Pa, which is 100 nm to the left of
Pb, and we calculated the power of the left-going light at Pa. Reflectivity is defined as the ratio of this
power to the launched power. Position Pdis located at a distance lMabove Pc. When lM¼ 100 nm,
we calculated the power of the light at Pd. Transmittance is defined as the ratio of this power to the
launched power. Fig. 4(a) shows the reflectivity and the transmittance with respect to wS. The
reflectivity increases as the transmittance decreases, and vice versa. Their sum remains almost constant and is smaller than 1 because of a loss in the region between Paand Pd. The increase in
reflectivity with wSis similar to what is observed in a 90direct bend of a MIM waveguide [7]. As the
insulator width of the MIM waveguide increases, the transmission through the 90 direct bend
decreases while the reflection from the bend increases. (It was also confirmed in our numerical simulation of the 90 direct bend of the MIM waveguide.)
Next, we calculated the excess loss Lb1of the MISIM waveguide with one 90 direct bend as a
function of lM. The excess loss Lb1is defined as the subtraction of½M ð100 nm þ wSþ 2tIþ lMÞ
from the insertion loss (in dB) of the structure between Pa and Pd. Fig. 4(b) and (c) shows the
calculated curves of Lb1for a few values of wS within the range [40 nm, 220 nm]. As wS increases
up to 130 nm, Lb1at lM ¼ 100 nm increases due to the increase in reflectivity. For wS 130 nm, Lb1
slightly increases initially with lM and soon becomes almost constant. However, as wS increases
further, Lb1at lM ¼ 100 nm decreases due to the decrease in reflectivity. For wS 9 130 nm, Lb1keeps
increasing with lM. This is different from what is expected from ordinary excess losses.
To find a reason for the increase of Lb1 with lM, we calculated the electric field distribution of the
transmitted light along the MISIM waveguide with the hybrid plasmonic mode launched at Pa. For
Fig. 3. Experimental and calculated values of Lb2 with respect to wS. The experimental values are
represented by the red square symbols with error bars. The theoretical values obtained from the 3-D FDTD simulation of the structure in Fig. 2(a) are also represented by the black solid lines with the circle symbols. The triangle symbols represent the calculated excess losses of the realized structure in Fig. 2(b) where the bends have the rounded corners.
different values of wS, Fig. 5(a) shows the distributions of Re½Ex after Pc, where Ex represents the
x -component of the electric field, on the xy -plane at z¼ 195 nm. The insets in Fig. 5(a) show the distributions of Re½Ex on the xz-plane at the positions denoted by the dashed lines. As wS
increases, the distributions become more and more asymmetric about the z-axis. For example, the distribution is almost symmetric for wS¼ 40 nm; however, it is almost antisymmetric for
wS ¼ 220 nm. After the bend, not only the hybrid plasmonic mode but also antisymmetric radiation
modes are excited. For more information, modes that exist in a bounded region containing the MISIM waveguide were analyzed by using the mode solver of FDTD Solutions, which is based on the finite-difference method. For wS G 230 nm, the hybrid plasmonic mode is the only guided mode
of the MISIM waveguide. Other modes have effective indexes with real parts smaller than the refractive index of the buried oxide or substrate. Thus, they are radiation modes whose fields radiate into the substrate. The distributions of Re½Ex of antisymmetric radiation modes are shown in
Fig. 5(b), and their effective indexesðNaÞ are summarized in Table 1 along with those ðNhÞ of the
hybrid plasmonic mode. As wS decreases, the imaginary part of Naincreases so that the decay of
the antisymmetric radiation mode becomes fast.
As deduced in Figs. 4 and 5, for wS G 130 nm, the hybrid plasmonic mode incident on the bend is
mainly transferred and reflected to the same mode. Although antisymmetric radiation modes are excited because of the bend, they decay out rapidly. However, for wS 9 130 nm, antisymmetric
radiation modes are dominantly excited after the bend. In this case, the bend behaves similarly as a mode converter. Hence, the excess loss Lb1 for wS 9 130 nm means how efficiently the hybrid
plasmonic mode is converted to antisymmetric radiation modes and how fast they decay compared with the hybrid plasmonic mode. Since the imaginary part of Na is larger than that of Nh, Lb1
increases with lM. The dominant excitation of antisymmetric radiation modes for wS 9 130 nm might
be explained intuitively as follows. A large portion of the power carried by the MISIM waveguide mode is transported along the insulator. Between Pb and Pc, the part of the light along the outer
insulator travels a longer distance than the part of the light along the inner insulator. The optical path
Fig. 4. (a) Reflectivity and transmittance of one 90direct bend versus w
S. The sum of the reflectivity
and the transmittance is also drawn together. (b) and (c) Calculated relations of Lb1to lMfor several
values of wSin the case of the MISIM waveguide with one 90direct bend. (d) Calculated relations of
Lb2to lM 2for several values of wSin the case of the MISIM waveguide with the two consecutive 90
difference between the two parts is about 2Re½NhðwSþ tIÞ. For wSabout 160 nm, it is close to half
the wavelength so that the two parts have a phase difference of at Pc. In this way, the hybrid
plasmonic mode at Pb is converted to antisymmetric radiation modes. Based on this intuitive
explanation, in the next section, we modify the 90direct bend with a large value of w
Sto reduce its
excess loss.
Fig. 5. (a) Distributions of Re½Ex on the xy -plane at z ¼ 195 nm after the 90direct bends for wS¼ 40,
70, 100, 160, 190, and 220 nm. The insets show the distributions of Re½Ex on the xz-plane at the
positions denoted by the dashed lines. (b) Distributions of Re½Ex of antisymmetric radiation modes for
the same values of wSas those in (a).
TABLE 1
b2 b1
slightly due to the second bend. In addition, Lb2 increases with lM2 since antisymmetric radiation
modes with propagation losses larger than that of the hybrid plasmonic mode travel between the two bends.
As shown in the inset in Fig. 2(b), the outer and inner corners of the realized 90direct bend are not sharp, but they are rounded. Such rounded corners make the experimental values of Lb2smaller
than the calculated values. We modified the simulated structure of the 90 direct bend to make it close to the realized one, and then, we calculated Lb2. The calculated values of Lb2 are 14.8, 7.4,
and 4.6 dB for wS¼ 160, 190, and 220 nm, respectively. They are represented in Fig. 3 and in good
agreement with the experimental values.
Through the various calculations, we have shown that the reflection from the 90direct bend is a main loss mechanism of the 90direct bend for wS G 130 nm. This explains the increase of Lb2 in
Fig. 3. When the two bends are connected, the excess loss due to themðLb2Þ changes significantly
with the distance between themðlM 2Þ because of the multiple reflections. For wS 9 130 nm, the 90
direct bend causes the conversion between the hybrid plasmonic mode and antisymmetric radiation modes. Lb2 increases with lM2 because of the large propagation losses of antisymmetric radiation
modes. Hence, the mode conversion is a main loss mechanism of the 90 direct bends for
wS 9 130 nm. This explains the decrease of Lb2 in Fig. 3.
4. Modified 90
Direct Bend
The simulation results show that the MISIM waveguide with the narrow Si line is better for the 90 direct bend than that with the wide Si line from the viewpoint of excess losses. For example, as shown in Fig. 3, Lb2¼ 2:1 dB for wS¼ 40 nm, but Lb2¼ 10:8 dB for wS¼ 190 nm. Although the
90 direct bend with wS¼ 40 nm causes a small excess loss, its total insertion loss, which is the
sum of the excess loss and the total propagation loss, is large. This is because the propagation loss of the MISIM waveguide increases as wSdecreases. In addition, the MISIM waveguide devices with
narrow Si lines require an additional fabrication process such as photoresist trimming, compared with those with wide Si lines. Therefore, for small total insertion losses and ease of fabrication, the 90 direct bend of the MISIM waveguide with the wide Si line must be modified to suppress the
mode conversion.
Using the aforementioned explanation of the excitation of antisymmetric radiation modes, we modified the bend as shown in Fig. 6(a). The modified bend has two protrusions of length wS=2 on
its outer corner. Except for these protrusions, the structure in Fig. 6(a) is the same as the structure in Fig. 2(a), which was used to get the result in Fig. 3. The protrusions may be considered to make the optical path length along the outer insulator about one wavelength longer than that along the inner insulator. Consequently, the two parts of the light traveling along the inner and outer insulators are in phase. Hence, the excitation of antisymmetric radiation modes seems to be suppressed. This can be checked in Fig. 6(b) and (c). The distribution of Re½Ex after the modified bend is almost
symmetric in contrast to that after the simple bend in Fig. 5(a). The distribution of Re½Hz, where Hz
is the real part of the z-component of the magnetic field, also indicates that the hybrid plasmonic mode is well excited after the modified bends. In this way, the excess loss of the modified bends can be reduced. When wS ¼ 190 nm, the structure in Fig. 6(a) has the calculated excess loss of
However, the total insertion loss of the structure in Fig. 6(a) is 3.1 dB smaller than that of the structure in Fig. 2(a). These results indicate that the modification improves the performance of the 90direct bend of the MISIM waveguide with the wide Si line. They also indicate that the explanation based on the excitation of antisymmetric radiation modes is reasonable. Finally, it is meaningful to compare the modified bend and a Si photonic waveguide bend. The single modified bend has an excess loss of about 1.3 dB while it occupies an area ofð3wS=2þ 2tIÞ2¼ 0:12 m2. However, the
90 curved bend of a Si photonic waveguide has an excess loss of about 0.1 dB if its bending radius is 1 m while it occupies an area of 1.56 m2 [20]. Therefore, the modified bend is more
advantageous in respect of compactness than the curved bend although the former has a larger excess loss than the latter.
5. Conclusion
We fabricated the 90 direct bends of the uncovered MISIM waveguides, using fully standard
CMOS technology without an additional photoresist trimming process. We measured the excess loss of the two consecutive 90 direct bends, which is 11, 7.4, and 4.5 dB for w
S ffi 160, 190, and
220 nm, respectively. Through the various calculations based on the 3-D FDTD method, newly we have investigated the loss mechanisms of the 90 direct bends. If the Si line of the MISIM
wave-guide is narrower than 130 nm, the excess loss of the 90direct bend is caused by the reflection from the bend. If the Si line is wider than 130 nm, the excess loss of the two consecutive bends is caused by the excitation of antisymmetric radiation modes between the bends. Our investigation has indicated that a narrow Si line (e.g., with a width of 40 nm) is desirable for reducing the excess loss of the 90direct bend. However, a wide Si line (e.g., with a width of 190 nm) is better for ease of fabrication and small propagation losses. Hence, for the MISIM waveguide with the wide Si line, we have proposed the modified 90direct bend. Based on the numerical simulation, we have confirmed that it has small excess loss similar to that of the simple 90 direct bend of the MISIM waveguide
with the narrow Si line. It is promising in that it is easy to fabricate and has a small total insertion loss, in comparison with the 90 direct bend of the MISIM waveguide with the narrow Si line.
References
[1] M. L. Brongersma and V. M. Shalaev,BThe case for plasmonics,[ Science, vol. 328, no. 5977, pp. 440–441, Apr. 2010. [2] E. Ozbay,BPlasmonics: Merging photonics and electronics at nanoscale dimensions,[ Science, vol. 311, no. 5758,
pp. 189–193, Jan. 2006.
[3] M. Dragoman and D. Dragoman, BPlasmonics: Applications to nanoscale terahertz and optical devices,[ Prog. Quantum Electron., vol. 32, no. 1, pp. 1–41, Jan. 2008.
[4] S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, BChannel plasmon subwavelength waveguide components including interferometers and ring resonators,[ Nature, vol. 440, no. 7083, pp. 508–511, Mar. 2006.
[5] T. Holmgaard and S. I. Bozhevolnyi,BTheoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,[ Phys. Rev. B, vol. 75, no. 24, pp. 245405-1–245405-12, Jun. 2007.
Fig. 6. (a) Schematic diagram of the structure of the MISIM waveguide with the modified bends on the xy -plane at z¼ 195 nm. (b) Distribution of Re½Ex on the xy -plane at z ¼ 195 nm after the modified 90
direct bend with wS¼ 190 nm. The inset shows the distribution of Re½Ex on the xz-plane at the position
Opt. Exp., vol. 17, no. 19, pp. 16 646–16 653, Sep. 2009.
[13] M. Wu, Z. Han, and V. Van,BConductor-gap-silicon plasmonic waveguides and passive components at subwavelength scale,[ Opt. Exp., vol. 18, no. 11, pp. 11 728–11 736, May 2010.
[14] D. Dai and S. He,BLow-loss hybrid plasmonic waveguide with double low-index nano-slots,[ Opt. Exp., vol. 18, no. 17, pp. 17 958–17 966, Aug. 2010.
[15] X.-Y. Zhang, A. Hu, J. Z. Wen, T. Zhang, X.-J. Xue, Y. Zhou, and W. W. Duley,BNumerical analysis of deep sub-wavelength integrated plasmonic devices based on semiconductor–insulator–metal strip waveguides,[ Opt. Exp., vol. 18, no. 18, pp. 18 945–18 959, Aug. 2010.
[16] M.-S. Kwon,BMetal–insulator–silicon–insulator–metal waveguides compatible with standard CMOS technology,[ Opt. Exp., vol. 19, no. 9, pp. 8379–8393, Apr. 2011.
[17] M.-S. Kwon, J.-S. Shin, S.-Y. Shin, and W.-G. Lee,BCharacterizations of realized metal–insulator–silicon–insulator– metal waveguides and nanochannel fabrication via insulator removal,[ Opt. Exp., vol. 20, no. 20, pp. 21 875–21 887, Sep. 2012.
[18] S. Zhu, T. Y. Liow, G. Q. Lo, and D. L. Kwong,BSilicon-based horizontal nanoplasmonic slot waveguides for on-chip integration,[ Opt. Exp., vol. 19, no. 9, pp. 8888–8902, Apr. 2011.
[19] S. Zhu, G. Q. Lo, and D. L. Kwong,BComponents for silicon plasmonic nanocircuits based on horizontal Cu-SiO2-Si-SiO2-Cu nanoplasmonic waveguides,[ Opt. Exp., vol. 20, no. 6, pp. 5867–5881, Mar. 2012.
[20] Z. Sheng, D. Dai, and S. He,BComparative study of losses in ultrasharp silicon-on-insulator nanowire bends,[ IEEE J. Sel. Topics Quantum Electron., vol. 15, no. 5, pp. 1406–1412, Sep./Oct. 2009.
